Problem: Simplify the following expression: $ a = \dfrac{2}{9} + \dfrac{p + 8}{10p} $
Answer: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{10p}{10p}$ $ \dfrac{2}{9} \times \dfrac{10p}{10p} = \dfrac{20p}{90p} $ Multiply the second expression by $\dfrac{9}{9}$ $ \dfrac{p + 8}{10p} \times \dfrac{9}{9} = \dfrac{9p + 72}{90p} $ Therefore $ a = \dfrac{20p}{90p} + \dfrac{9p + 72}{90p} $ Now the expressions have the same denominator we can simply add the numerators: $a = \dfrac{20p + 9p + 72}{90p} $ $a = \dfrac{29p + 72}{90p}$